Certainly the tone adopted by any author in their work is a deliberate choice, designed to enhance the impact of the work. This memorable recollection of one man's punishment during the Civil War is no exception. You might want to think about what mood is created and how it is sustained. For example, in the first section of the story, it is clear that a solemn mood is created as the soldiers make their preparations to hang Peyton Farquhar. Note the following extract:
The company faced the bridge, staring stonily, motionless. The sentinels, facing the banks of the stream, might have been statues to adorn the bridge. The captain stood with folded arms, silent, observing the work of his subordinates, but making no sign. Death is a dignitary who when he comes announced is to be received with formal manifestations of respect, even by those most familiar with him. In the code of military etiquette, silence and fixity are forms of deference.
Clearly, the formal diction and the personification of death as a dignitary evoke the sombre, solemn mood that is suitable to the hanging that is just about to happen. Note how words such as "stonily," "motionless" and the description of the sentinels as "statues" reinforce the state and ceremony of the occasion of welcoming death. The tone, then, always helps to increase the impact of the story, as it conveys a mood that is richly suggestive to the reader.